Abstract
In a very recent work, G. E. Andrews defined the combinatorial objects which he called singular overpartitions with the goal of presenting a general theorem for overpartitions which is analogous to theorems of Rogers-Ramanujan type for ordinary partitions with restricted successive ranks. As a small part of his work, Andrews noted two congruences modulo 3 which followed from elementary generating function manipulations. In this work, we show that Andrews' results modulo 3 are two examples of an infinite family of congruences modulo 3 which hold for that particular function. We also expand the consideration of such arithmetic properties to other functions which are part of Andrews' framework for singular overpartitions.
Original language | English (US) |
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Pages (from-to) | 1463-1476 |
Number of pages | 14 |
Journal | International Journal of Number Theory |
Volume | 11 |
Issue number | 5 |
DOIs | |
State | Published - Aug 5 2015 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory